Quanto é ?log ∛9
√27
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Olá Carol!
![\\ \mathsf{\log_{\sqrt{27}} \sqrt[3]{9} =} \\\\ \mathsf{\log_{27^{\frac{1}{2}}} 9^{\frac{1}{3}} =} \\\\ \mathsf{\log_{(3^3)^{\frac{1}{2}}} (3^2)^{\frac{1}{3}} =} \\\\ \mathsf{\log_{3^{\frac{3}{2}}} 3^{\frac{2}{3}} =} \\\\ \mathsf{\frac{2}{3} \cdot \log_3 3^{\frac{2}{3}} =}](https://tex.z-dn.net/?f=%5C%5C+%5Cmathsf%7B%5Clog_%7B%5Csqrt%7B27%7D%7D+%5Csqrt%5B3%5D%7B9%7D+%3D%7D+%5C%5C%5C%5C+%5Cmathsf%7B%5Clog_%7B27%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D+9%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D+%3D%7D+%5C%5C%5C%5C+%5Cmathsf%7B%5Clog_%7B%283%5E3%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D+%283%5E2%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D+%3D%7D+%5C%5C%5C%5C+%5Cmathsf%7B%5Clog_%7B3%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D+3%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D+%3D%7D+%5C%5C%5C%5C+%5Cmathsf%7B%5Cfrac%7B2%7D%7B3%7D+%5Ccdot+%5Clog_3+3%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D+%3D%7D "\\ \mathsf{\log_{\sqrt{27}} \sqrt[3]{9} =} \\\\ \mathsf{\log_{27^{\frac{1}{2}}} 9^{\frac{1}{3}} =} \\\\ \mathsf{\log_{(3^3)^{\frac{1}{2}}} (3^2)^{\frac{1}{3}} =} \\\\ \mathsf{\log_{3^{\frac{3}{2}}} 3^{\frac{2}{3}} =} \\\\ \mathsf{\frac{2}{3} \cdot \log_3 3^{\frac{2}{3}} =}")
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